Pelican Parts Forums - Strange Idle Issue

Hello - Brand new Porsche owner here.

Background:

I recently purchased a 1981 Porsche 911SC with 78,000 miles. It has decent documentation - 3rd owner - Ive driven the car roughly 300 miles

Motor was out for a rebuild at 70,000 miles in 2005 (12 years ago)
There were many things replaced (Long list) - but from the CIS main components the following were replaced:

O2 sensor
Fuel pump
Rebuilt Fuel Distributor head
remanufactured Warm up regulator (WUR Model 0438140090)

Situation:
I am having difficulty diagnosing a rough idle situation.

The car will cold start with foot pedal half way to floor holding for 30 seconds or so to smooth out idle (a little rough to start) - but then the car runs phenomenal.. 900 revs at idle (dead straight) and can drive for hours. I have taken 4 long trips with one lasting 2 1/2 hours with no idling problems or performance issues..

However - Once I shut the vehicle off and try to restart - the car runs horrible. It will start with no problems - but will not idle. It will oscillate ("hunt" or "lope") up and down around 500 to 700 rpms and performance will suffer - I have little backfires or sputtering that happens upon acceleration. Its still drivable - as I drove it 30 minutes to get home after a car show this way - however it doesn't correct itself - it ran rough and idled rough the entire way.

If I leave the car overnight - It will start and idle at the 900rpm range - running like the car I imagined.. BUT shut it down to fill up with gas - then it runs like crap..

Any suggestions to the components I should test or change? :confused: Im not sure where to start - and this issue severely diminishes the use of this car..

I have searched and read through many threads (so I am working on educating myself) - I ordered a CIS fuel pressure tester and I can use a multimeter. I also have the Bentley manual. The CIS system is all new to me - so I made need some step by step help in performing the tests..